Thermodynamics and Criticality of Noncommutative RN-AdS Black Holes

TL;DR

This work demonstrates that Reissner–Nordström–AdS black holes in noncommutative spacetime with Lorentzian-smearing exhibit thermodynamic behavior closely resembling Van der Waals fluids when analyzed in an extended phase space. By deriving large-$r$ expansions for the smeared mass and charge functions, the authors obtain a modified metric and proceed to compute $M$, $T_H$, $S$, and $C_p$, revealing NC-induced stability structures and curvature regularization effects. In the extended framework, they derive the $P$–$V$ equation of state and critical quantities, showing a universal ratio for the NC-corrected system and reproducing RN–AdS limits as NC effects vanish. The Joule–Thomson expansion further confirms universal features akin to ordinary charged AdS black holes, highlighting the robustness of the NC modifications. Overall, the work provides a coherent thermodynamic portrait of NC RN–AdS black holes and their phase structure, with potential implications for holography and quantum gravity phenomenology.

Abstract

Inspired by string theory topics, we investigate the Reissner Nordstrom AdS black holes in noncommutative spacetime with Lorentzian smeared distributions. Concretely, we study certain thermodynamic properties including the criticality behaviors by computing the relevant quantities. For large radius approximations, we first derive the asymptotic expansions of the mass and charge functions appearing in the metric function of such black holes. Then, we approach the thermodynamics in the extended phase space. After the stability discussion, we examine the P V criticality in noncommutative geometry by calculating the corresponding thermodynamic quantities. As a result, we show that the proposed black holes exhibit certain similarities with Van der Waals fluid systems. Finally, we present a discussion on the Joule Thomson expansion showing perfect universality results appearing in charged AdS black holes.

Figures (7)

• Figure 1: Effect of the charge parameter $Q$ and $a$ on the metric function $f(r)$ for $M=1$ and $\Lambda=-20$.
• Figure 2: Profile of the embedding diagram within different values of the correction parameter $a$.
• Figure 3: Effect of the charge parameter $Q$ and $a$ on the Hawking temperature $T$ as a function of $r_h$ by taking $\Lambda=-50$.
• Figure 4: Effect of the charge parameter $Q$ and the NC parameter $a$ on the heat capacity as a function of $r_h$ for $\Lambda=-0.1$.
• Figure 5: Pressure in terms of $v$ for different values of $T$ and $b$ with $Q=0.4$.